On the eighth day of the consecration of the Mishkan, Nadav and Avihu sinned and defiled the Mishkan. As a consequence, God sent Aharon to atone on behalf of the Kohanim, the people of Israel and the Mishkan. Aharon's order of the atonement service serves as the model for the Kohen Gadol's service on Yom Kippur.
The sin of Aharon's sons in the Mishkan and their resulting death which defiled the Mishkan, necessitated an immediate atonement. Therefore God commands that Aharon must atone for their sin and the sin of his household. He brings a sin offering, in order to "atone for himself and for his household." (Lev. 16:6)
In addition, atonement is also needed on behalf of the people of Israel: "And he shall atone for himself, for his household, and for all the congregation of Israel." (Lev. 16:17), and also for the Mishkan which was defiled by the sin and the impurity: "He shall do likewise to the Tent of Meeting, which dwells with them amidst their defilements." (Lev. 16:16).
At the end of the incident, the Torah states that atonement is not only required in this particular event as an immediate solution to the current situation brought about by Nadav and Avihu's sin, but also for future generations. Therefore, the order of Aharon's service following the death of his sons is the model for the service of the Kohen Gadol on Yom Kippur.